{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:AZYWMDPN2USPKBCIMB4WV2M5KY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2fb2d69df9dcd4b761343bb49616d52d25b8105c6730f91d7d29e91fad706ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-16T12:16:24Z","title_canon_sha256":"56610c66712864867612bcd96c57f4eac0cb94e5e40af0c406c2649ff91ba56b"},"schema_version":"1.0","source":{"id":"0904.2475","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0904.2475","created_at":"2026-05-18T03:38:05Z"},{"alias_kind":"arxiv_version","alias_value":"0904.2475v1","created_at":"2026-05-18T03:38:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.2475","created_at":"2026-05-18T03:38:05Z"},{"alias_kind":"pith_short_12","alias_value":"AZYWMDPN2USP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"AZYWMDPN2USPKBCI","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"AZYWMDPN","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:064d3ed8295ea6fddfab109ff9f3454f8ac421bbb4e319707a7edede862b1490","target":"graph","created_at":"2026-05-18T03:38:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"A conformal immersion of a 2-torus into the 4-sphere is characterized by an auxiliary Riemann surface, its spectral curve. This complex curve encodes the monodromies of a certain Dirac type operator on a quaternionic line bundle associated to the immersion. The paper provides a detailed description of the geometry and asymptotic behavior of the spectral curve. If this curve has finite genus the Dirichlet energy of a map from a 2-torus to the 2-sphere or the Willmore energy of an immersion from a 2-torus into the 4-sphere is given by the residue of a specific meromorphic differential on the cur","authors_text":"Christoph Bohle, Franz Pedit, Ulrich Pinkall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-16T12:16:24Z","title":"The spectral curve of a quaternionic holomorphic line bundle over a 2-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.2475","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8b6f89ed3854678e8827b49ff89d9aad2a5236c1f307f11adba33cdd6094f644","target":"record","created_at":"2026-05-18T03:38:05Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2fb2d69df9dcd4b761343bb49616d52d25b8105c6730f91d7d29e91fad706ba3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-04-16T12:16:24Z","title_canon_sha256":"56610c66712864867612bcd96c57f4eac0cb94e5e40af0c406c2649ff91ba56b"},"schema_version":"1.0","source":{"id":"0904.2475","kind":"arxiv","version":1}},"canonical_sha256":"0671660dedd524f5044860796ae99d5608a41bec9b85e7c035d937646497059b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0671660dedd524f5044860796ae99d5608a41bec9b85e7c035d937646497059b","first_computed_at":"2026-05-18T03:38:05.245840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:05.245840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QabXEXa/oR2ii16ePKcGL+81qePj++8z1UF9Dp6v+jYYOUB/l2Lug/xzbMnMIAW1PSfovyycV2P9J+V1xN9gBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:05.246445Z","signed_message":"canonical_sha256_bytes"},"source_id":"0904.2475","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b6f89ed3854678e8827b49ff89d9aad2a5236c1f307f11adba33cdd6094f644","sha256:064d3ed8295ea6fddfab109ff9f3454f8ac421bbb4e319707a7edede862b1490"],"state_sha256":"3cfa1acce22b90748658d7db910c7eb34b677c6b44062678c63eb7c7535c7eff"}